I don't know the terms for educational establishments in other countries.
Schooling in UK
Nursery School/ playgroup ...up to 4/5yrs
Infant school ... 4/5 to 7yrs
Junior School ... 7 to 11yrs
Secondary School ... 11 to 16 yrs
6th form College ... 16 to 18 yrs
University (aka Uni)
In some areas we have Comprehensive Schools for all ability levels,and Grammar schools for more able children from 11 yrs up.
There are other types of school as well - Middle school for ages 9 to 13 yrs - and Independent Schools which are not under state control
There is another category of education in the UK called Home Schooling - I did this with my son (now grown up) from birth to age 12 yrs - he then joined a local school so that he could study subjects that I did not feel competent to teach. Not many people do this but it is actually legal.
There are also really confusing categories for naming types of schools:-
State Schools which are for anybody regardless of income...
Public Schools - most public schools are fee paying and are in the private sector (such as Eton and Harrow)
We have 'GCSE' and 'A' levels at 16yrs and 18 yrs ...then University degree....though there are a host of other qualifications as well.

Just to confuse the issue - Scotland has a different way of naming its types of schools and scholastic qualifications!!!
I would be interested to know how levels of attainment are named in other countries...